A formal language approach for a 3D curve representation

A formal language approach for representing three-dimensional (3D) curves is presented. Based on the chain code for representing 3D curves defined in [1], we propose an approach for mapping 3D curves into strings. This mapping allows us to have a unique curve descriptor, which is invariant under translation and rotation. Also, it is possible to use inverse and mirroring operators and the use of formal language techniques for 3D curve generation and analysis. Finally, we present a result of this approach to represent and to generate polygonal sequences convergent to cube-filling Hilbert curves